Topology-enhanced loss improves 3D object reconstruction from 2D images.
problem Challenges in reconstructing 3D objects from 2D images, especially capturing shape information.
method Integrates multi-scale topological features into the reconstruction loss using cubical complexes and optimal transport distance.
result Topology-aware loss substantially improves 3D reconstruction quality.
Optimizing full likelihoods adapts loss scales and shapes for robust modeling.
problem Rigid loss functions limit model adaptability and robustness.
method Optimize full likelihoods with adjustable parameters.
result Adaptive tuning of loss scales and shapes improves model robustness.
Proposes DILATE and STRIPE++ for precise time series forecasting.
problem Non-stationary signals with sudden changes.
method Incorporates shape and temporal criteria in deep learning models.
result Improves precision in deterministic and probabilistic forecasting.
New method for high-fidelity shape representations from raw data.
problem Creating accurate shape representations from raw data.
method A simple loss function encouraging neural network to vanish on input point cloud and have unit norm gradient.
result Our method produces high-fidelity, smooth, and natural zero level set surfaces.
New approach shapes error distribution in long-term forecasting.
problem Disparate error distributions in recent transformer models.
method Loss shaping constraints to respect upper bounds on loss at each time-step.
result Competitive average performance with shaped error distribution.
Investigates conditions for risk or utility functionals to be sensitive to large losses.
problem Conditions for risk or utility functionals to be sensitive to large losses.
method Analyzes sensitivity to large losses for various risk and utility functionals.
result Value at Risk and Expected Shortfall generally fail to be sensitive to large losses, but expected utility functionals and certain adjusted versions are sensitive.
New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of shapes without causing a possibly large loss of information. Dictionary learning and sparse coding allow us to reduce the high dimensional space of shapes into a manageable low dimensional continuous vector space. Statisti…
PINNs solve differential geometry problems in complex shapes.
problem Solving differential geometry problems in complex shapes.
method Training neural networks with loss functions inspired by differential conditions.
result PINNs are effective for differential geometry problems.
A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However, this shape has not yet been examined in detail. This work shows empirically that…
This paper addresses the problem of time series forecasting for non-stationary signals and multiple future steps prediction. To handle this challenging task, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective function for training deep neural networks. DILATE aims at accurately predicting s…
New method learns shape correspondences robustly from raw geometry.
problem Inaccurate and poor generalization of shape correspondences.
method Learning-based approach with feature-extraction network and functional map representation.
result Robust and accurate shape correspondence learning with less training data.
LIMP learns latent shapes with metric preservation, improving generative models.
problem Insufficient training data for high-fidelity latent representations.
method Metric preservation as a prior, geometric distortion criterion, geodesic loss.
result Synthetic samples of higher quality achieved through metric preservation.
Paper tackles shape graph registration using neural networks.
problem Constrained registration of shape graphs with varying nodes and edges.
method Shape-Graph Matching Network (SGM-net) with an elastic shape metric loss function.
result State-of-the-art matching performance and reduced computational cost.
A new tail-shape index based on Value at Risk and Expected Shortfall.
problem Measuring and comparing tail behavior of loss distributions.
method Introducing a new θ-index based on equal level relationships between Value at Risk and Expected Shortfall. result The θ-index provides a level-dependent, scale-free measure of upper tail behavior. New deep learning method preserves orientation in shape matching.
problem Symmetry issues in shape matching.
method Orientation-aware functional maps using complex functional representations and DiffusionNet.
result Stable correspondence predictions with robust orientation preservation.
Study optimal consumption for loss-averse agents considering past spending peaks.
problem Optimal consumption for loss-averse agents with reference to past spending maximum.
method Adopted S-shaped utility, concave envelope, HJB variational inequality, dual transform, and smooth-fit conditions.
result Obtained piecewise closed-form solutions for optimal consumption and investment control.
We introduce a wide and deep neural network for prediction of progression from patients with mild cognitive impairment to Alzheimer's disease. Information from anatomical shape and tabular clinical data (demographics, biomarkers) are fused in a single neural network. The network is invariant to shape transformations an…
This study explores star-shaped regularizers learned from critic-based losses.
problem Understanding the structure of regularizers learned from critic-based losses.
method Optimizing critic-based loss functions over star-shaped regularizers.
result Derives exact expressions for optimal regularizers in certain cases.
A new method for analyzing shapes and forms using additive models on manifolds.
problem Analyzing shapes and forms under geometric transformations.
method Extending generalized additive regression to models for shapes/forms using squared geodesic distance and Riemannian L2-Boosting algorithm. result Automated model selection and intuitive visualization of covariate effects in shape/form space.
A new method for analyzing shapes using FDA techniques.
problem Statistical shape analysis of deformed contours.
method Functional Data Analysis (FDA) with basis expansion and principal component analysis.
result Successfully identifies deformation parameters and captures contour distributions.
The paper explores risk measures and arbitrage in financial markets.
problem Quantifying and managing risk in financial markets.
method Introduces new risk measure axioms and characterizes arbitrage conditions.
result Derives the consistent price interval for financial contracts.
This paper analyzes optimal consumption strategies for loss-averse investors with multiplicative habit formation.
problem Optimal consumption strategies for loss-averse investors with multiplicative habit formation.
method The study uses a concave envelope of the S-shaped utility function and a nonlinear free boundary problem to analyze the HJB equation.
result The paper provides optimal consumption and investment policies in feedback form.
Looped transformers outperform standard transformers in complex reasoning tasks due to a specific loss landscape geometry.
problem Understanding why looped transformers outperform standard transformers in complex reasoning tasks.
method Explained through loss landscape geometry, distinguishing between U-shaped and V-shaped valleys, and proposing SHIFT training strategy.
result Looped transformers' recursive architecture induces a River-V-Valley landscape, leading to better loss convergence and complex pattern learning.
Piecewise linear activations create many spurious local minima in neural networks.
problem Understanding the loss surface of neural networks with piecewise linear activations.
method Proved the existence of infinite spurious local minima and partitioned the loss surface into smooth cells.
result Piecewise linear activations create many spurious local minima that are invariant under a continuous path.
Neural network training relies on our ability to find "good" minimizers of highly non-convex loss functions. It is well-known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce mi…
We develop a tractable model of realization utility that studies the role of reference-dependent S-shaped preferences in a dynamic investment setting with reinvestment. Our model generates both voluntarily realized gains and losses. It makes specific predictions about the volume of gains and losses, the holding periods…
Study visualizes actor-critic loss landscapes for inventory optimization.
problem Difficulties in solving multi-store dynamic inventory control problems.
method Low-dimensional visualizations of actor loss function.
result Loss landscapes favor optimal policies in reinforcement learning.
New method estimates extreme outcomes in heavy-tailed data, breaking circular dependence.
problem Estimating outcomes for extreme events in heavy-tailed data.
method Proposes an ADRF estimator that includes a structured tail-shape output and a diagnostic to evaluate tail shape.
result Successfully reduces MAE in deep-tail and conditional-shortfall predictions.
Study compares geometric approaches for shape and deformation statistics.
problem Characterizing statistical models of shapes and deformations.
method Information geometry and Wasserstein geometry.
result Wasserstein estimator is robust against waveform perturbation.
Typically, loss functions, regularization mechanisms and other important aspects of training parametric models are chosen heuristically from a limited set of options. In this paper, we take the first step towards automating this process, with the view of producing models which train faster and more robustly. Concretely…
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time sy…
Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of pena…
A censored transformed model for proportional outcomes with boundary mass and an application to loss given default modeling.
problem Modeling proportional outcomes with boundary mass in loss given default (LGD) modeling.
method Zero-one censored transformed normal (ZOC-TN) model.
result Captures a wider range of qualitative density shapes than benchmark models while being parsimonious, computationally efficient, and numerically stable.
It has been argued in the past that high-dimensional neural networks do not exhibit local minima capable of trapping an optimisation algorithm. However, the relationship between loss surface modality and the neural architecture parameters, such as the number of hidden neurons per layer and the number of hidden layers, …
Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
problem Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
method Identifying entropic barriers arising from the interplay between curvature variations along low-loss paths and noise in optimization dynamics.
result Curvature-induced entropic forces bias noisy dynamics back toward the endpoints, explaining the confinement and connectivity of solutions.
Improved time series forecasting with expert loss integration.
problem Enhancing time series forecasting accuracy and efficiency.
method Adaptive Mixture-of-Experts framework with expert-specific loss integration and online learning.
result Significantly improved forecasting accuracy and computational efficiency.
New framework optimizes classification trees with logistic loss and ℓ1 regularization.
problem Improving interpretability and generalization of classification trees.
method Developed a generalized framework for CTs, incorporating logistic loss and ℓ1 regularization. result Optimal Logistic Tree model outperforms state-of-the-art MIP-based approaches in terms of interpretability and generalization.
New algorithm for robust density estimation in corrupted data.
problem Density estimation in the presence of adversarial corruption.
method Proposes an algorithm for constructing a density estimator within a star-shaped density class, derived minimax bounds for estimation.
result Obtained minimax upper and lower bounds for density estimation under adversarial corruption.
EPD method accurately captures parameter distributions from RCS data.
problem Limitations of traditional methods in estimating parameter distributions from RCS data.
method EPD method generates synthetic trajectories, estimates parameters, and selects parameters based on discrepancy.
result EPD provides accurate distribution of parameters without data loss.
Study investigates overparametrization in survival models, revealing complex loss behavior.
problem Understanding overparametrization in survival models through interpolation.
method Defined interpolation and finite-norm interpolation, rigorously analyzed four survival models.
result Overparametrization can lead to improved performance in survival models, contrary to classical learning theory.
Improved loss functions adapt to weight-space anisotropy, outperforming isotropic counterparts.
problem Adapting to the anisotropic nature of deep weight spaces for better performance.
method Refined local entropic loss functions restricted to a subset of weights, exploiting anisotropy.
result Partial local entropies outperform isotropic counterparts on image classification tasks.
Adaptive rerouting reshapes impacts of maritime chokepoint disruptions
problem How disruptions to shipping traffic at chokepoints affect global economy
method Empirically calibrated full-scale agent-based model of global commercial shipping fleet
result Rerouting changes arrival losses under chokepoint closures
The paper presents a multi-power law for predicting loss curves across different learning rate schedules.
problem Understanding and optimizing the relationship between model performance and hyperparameters, especially learning rates.
method Proposes a multi-power law that combines power laws based on the sum of learning rates and additional laws for loss reduction due to decay.
result The multi-power law accurately predicts loss curves for unseen learning rate schedules and finds a schedule that outperforms cosine learning rate.
The premorbid geometry of the mandible is of significant relevance in jaw reconstructive surgeries and occasionally unknown to the surgical team. In this paper, an optimization framework is introduced to train deep models for completion (reconstruction) of the missing segments of the bone based on the remaining healthy…
New algorithm identifies best arm in rested bandit setting.
problem Best arm identification in rested bandit with decreasing losses.
method Introduced a novel best arm identification problem and analyzed an arm elimination algorithm.
result Regret vanishes as time horizon increases, with convergence rate depending on expected loss function.
This research develops a new model for cyber risk and insurance pricing.
problem Accurate calculation of aggregate losses in cyber insurance pricing.
method A path-based k-generation risk contagion model in a tree-shaped network structure.
result Explicit expressions for mean and variance of local loss on a single path.
Uniform AMMs control loss in prediction markets.
problem Controlling loss in prediction markets.
method Loss-versus-rebalancing (LVR) framework and uniform AMMs.
result Uniform AMMs achieve proportional LVR to pool value.